Enumeration of Rooted Partial Subtrees

1. A method of executing instructions on at least one computing device in which the at least one computing device includes at least one processor and at least one memory, the method comprising: communicating instructions from the at least one memory to the at least one processor; and executing the communicated instructions on the at least one processor of the at least one computing device; wherein the communicated instructions comprise instructions to perform database processing; and wherein the executing the database processing instructions further comprises: representing stored content of the database, at least in part, as a complex tree hierarchy, wherein the complex tree hierarchy comprises a set of subtrees and/or partial subtrees, and wherein the set of the subtrees and/or the partial subtrees represent at least a portion of the stored content of the database in the complex tree hierarchy, wherein the set of the subtrees and/or the partial subtrees includes an enumeration of possible subtrees and/or partial subtrees of the complex tree hierarchy, wherein the enumeration of possible subtrees and/or partial subtrees includes multiple potential subtrees from a single node of the complex tree hierarchy; and associating symbols with respect to the set of the subtrees and/or the partial subtrees.

2. The method of claim 1 , wherein the symbols comprise numerals; and further comprising performing one or more operations on the stored content, wherein the performing the one or more operations on the stored content comprises performing one or more arithmetic operations on at least some of the numerals associated with the set of the subtrees and/or the partial subtrees.

3. The method of claim 1 , wherein the executing the database processing instructions further comprises: wherein the associating the symbols with the set of subtrees and/or the partial subtrees comprises providing relationships between the set of the subtrees and/or the partial subtrees.

4. The method of claim 3 , wherein the symbols comprise numerals and further comprising performing one or more operations on the stored content based, at least in part, on the relationships between the set of the subtrees and/or the partial subtrees.

5. The method of claim 1 , wherein the complex tree hierarchy comprises one or more subtrees coupled to the complex tree hierarchy, and wherein at least some of the one or more subtrees respectively comprise a set of partial subtrees.

6. The method of claim 5 , wherein the executing the database processing instructions further comprises: enumerating at least some of corresponding partial subtrees of the at least some of the one or more subtrees.

7. The method of claim 6 , wherein the symbols comprise numerals and further comprising performing one or more operations on the stored content based, at least in part, on relationships between the respective partial subtrees provided substantially in accordance with the numerals associated with the respective partial subtrees.

8. An apparatus comprising: at least one computing device in which the at least one computing device includes at least one processor and at least one memory; the at least one memory to communicate instructions to the at least one processor; the at least one processor to execute the communicated instructions; wherein the communicated instructions to be executed comprise instructions to perform database processing; and wherein the database processing instructions to be executed comprise instructions further to: represent stored content of the database, at least in part, as a complex tree hierarchy, the complex tree hierarchy to comprise a set of subtrees and/or partial subtrees, and the subtrees and/or the partial subtrees to represent at least a portion of the stored content of the database to be represented by the complex tree hierarchy, wherein the set of the subtrees and/or the partial subtrees includes an enumeration of possible subtrees and/or partial subtrees of the complex tree hierarchy, wherein the enumeration of possible subtrees and/or partial subtrees includes multiple potential subtrees from a single node of the complex tree hierarchy; and associate symbols with respect to the set of the subtrees and/or the partial subtrees.

9. The apparatus of claim 8 , wherein the symbols comprise numerals and the database processing instructions comprise further instructions to: perform one or more operations on the stored content; and compute one or more arithmetic operations on at least some of the numerals to be associated with the set of the subtrees and/or the partial subtrees.

10. The apparatus of claim 8 , wherein the symbols comprise numerals and the database processing instructions comprise further instructions to associate numerals with the set of the subtrees and/or the partial subtrees; and to relate the set of the subtrees and/or the partial subtrees based, at least in part, on the associated numerals.

11. The apparatus of claim 10 , wherein the database processing instructions comprise further instructions to perform one or more operations on the stored content, wherein to perform the one or more operations on the stored content to comprise to perform one or more operations based, at least in part, on the relationships between the set of the subtrees and/or the partial subtrees.

12. The apparatus of claim 8 , wherein the complex tree hierarchy is to comprise one or more subtrees to be coupled to the complex tree hierarchy, and wherein at least some of the one or more subtrees to comprise a set of corresponding partial subtrees.

13. The apparatus of claim 12 , wherein the database processing instructions comprise further instructions to: enumerate at least some of corresponding partial subtrees of the at least some of the one or more subtrees.

14. The apparatus of claim 13 , wherein the symbols comprise numerals and database processing instructions comprise further instructions to perform one or more operations on the stored content, wherein to perform the one or more operations on the stored content to comprise further instructions to perform one or more arithmetic operations, based, at least in part, on relationships between the respective partial subtrees established, at least in part by, numerals to be associated with the respective partial subtrees.

15. An article comprising: a non-transitory storage medium comprising: device-readable instructions stored thereon executable by at least one computing device, the at least one computing device comprising at least one processor and at least one memory, to: communicate instructions from the at least one memory to the at least one processor; and execute the to be communicated instructions on the at least one processor; wherein the to be communicated instructions to be executed to comprise instructions to perform database processing; and wherein the database processing instructions to be executed comprise instructions to: represent stored content of the database, at least in part, as a complex tree hierarchy, the complex tree hierarchy to comprise a set of subtrees and/or partial subtrees, and the set of the subtrees and/or the partial subtrees to represent, at least a portion of the stored content of the database to be represented by the complex tree hierarchy, wherein the set of the subtrees and/or the partial subtrees includes an enumeration of possible subtrees and/or partial subtrees of the complex tree hierarchy, wherein the enumeration of possible subtrees and/or partial subtrees includes multiple potential subtrees from a single node of the complex tree hierarchy; and associate symbols with respect to the set of the subtrees and/or the partial subtrees.

16. The non-transitory storage medium of claim 15 , wherein the symbols comprise numerals and the database processing instructions comprise further instructions to: perform one or more operations on the stored content; and compute one or more arithmetic operations on at least some of the numerals to be associated with the set of the subtrees and/or the partial subtrees.

17. The non-transitory storage medium of claim 15 , wherein the symbols to comprise numerals and the database processing instructions comprise further instructions to associate numerals with the set of the subtrees and/or partial subtrees; and to establish relationships between the set of the subtrees and/or the partial subtrees.

18. The non-transitory storage medium of claim 17 , wherein the database processing instructions to comprise further instructions to perform the one or more operations on the stored content, wherein the further instructions to manipulate the respective partial subtrees, based, at least in part, on numerals to be associated with the respective partial subtrees.

19. The non-transitory storage medium of claim 15 , wherein the complex tree hierarchy comprises one or more subtrees coupled to the complex tree hierarchy, at least some of the one or more subtrees to comprise a set of corresponding partial subtrees.

20. The non-transitory storage medium of claim 19 , wherein the database processing instructions comprise further instructions to: enumerate at least some of corresponding partial subtrees of the at least some of the one or more subtrees.